We find all possible isomorphisms and 3-birational maps (i.e., birational which induce an isomorphism between open subsets whose respective complements have codimension at least 3) moduli spaces of parabolic vector bundles with fixed degree. prove that every map can be described as a composition tensorization by line bundle, Hecke transformations, dualization, taking pullback the curves action ...

A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose roots are sought dominates the computation time, and additionally the Jacobian is sparse. One example of such a case is the solution of the discretized transpo...

This the original TEX file for my article Jacobian Varieties, published as Chapter VII of Arithmetic geometry (Storrs, Conn., 1984), 167–212, Springer, New York, 1986. The table of contents has been restored, some corrections and minor improvements to the exposition have been made, and an index has been added. The numbering is unchanged.

For any discrete, torsion-free subgroup Γ of Sp(n, 1) (resp. F−20 4 ) with no parabolic elements, we prove that H4n−1(Γ;V ) = 0 (resp. Hi(Γ;V ) = 0 for i = 13, 14, 15) for any Γ–module V . The main technical advance is a new bound on the p–Jacobian of the barycenter map of Besson–Courtois–Gallot. We also apply this estimate to obtain an inequality between the critical exponent and homological d...

In most robotic applications, tactile sensors are modeled as rigid matrices of adjacent pressure sensing elements so that the geometric deformations of their surfaces are neglected. This paper proposes to define these deformations as rotational and translational compliances that are later used as new tactile features for tactile servoing tasks. In fact, a novel two-layered inverse tactile Jacob...

We consider the Sobolev space X = W s,p(Sm;Sk−1). We prove the existence of a robust distributional Jacobian Ju for u ∈ X provided sp ≥ k−1; this generalizes a result of Bourgain, Brezis and the second author [10], where the case m = k is considered. In the critical case where sp = k − 1, we identify the image of the map X 3 u 7→ Ju. This extends a result of Alberti, Baldo and Orlandi [2] for s...

Contents 1. Introduction 1 1.1. Notation and Conventions 2 1.2. Brill-Noether varieties and Abel maps 4 1.3. Stability and semistability 6 2. Technical groundwork 9 2.1. Basic estimates 9 2.2. Basic cases 12 2.3. Divisors imposing independent conditions 14 3. Irreducibility and dimension 19 3.1. Irreducible components of the Theta divisor 19 3.2. Dimension of the image of the Abel map 24 4. Com...

For any discrete, torsion-free subgroup Γ of Sp(n, 1) (resp. F−20 4 ) with no parabolic elements, we prove that H4n−1(Γ;V ) = 0 (resp. Hi(Γ;V ) = 0 for i = 13, 14, 15) for any Γ–module V . The main technical advance is a new bound on the p–Jacobian of the barycenter map of Besson–Courtois–Gallot. We also apply this estimate to obtain an inequality between the critical exponent and homological d...

The Finite-time Lyapunov Exponent (FTLE) is a measure for the rate of separation of particles in time-dependent flow fields. It provides a valuable tool for the analysis of unsteady flows. Commonly it is defined based on the flow map, analyzing the separation of trajectories of nearby particles over a finite-time span. This paper proposes a localized definition of the FTLE using the Jacobian ma...

We shall call a polynomial map f : C → C a “coordinate” if there is a g such that (f, g) : C → C is a polynomial automorphism. Equivalently, by AbhyankarMoh and Suzuki, f has one and therefore all fibres isomorphic to C. Following [7] we call a polynomial f : C → C “rational” if the general fibres of f (and hence all fibres of f) are rational curves. The following theorem, which says that a rat...